Commons

You take the high road and I’ll take the low road. example 6⊲ Figure t shows two ramps which two balls will roll down. Comparetheir final speeds, when they reach point B. Assume frictionis negligible.⊲ Each ball loses some gravitational energy because of its decreasingheight above the earth, and conservation of energy saysthat it must gain an equal amount of kinetic energy (minus a littleheat created by friction). The balls lose the same amount ofheight, so their final speeds must be equal.t / Example 6.u / Example 7.The birth of stars example 7Orion is the easiest constellation to find. You can see it in thewinter, even if you live under the light-polluted skies of a big city.Figure u shows an interesting feature of this part of the sky thatyou can easily pick out with an ordinary camera (that’s how I tookthe picture) or a pair of binoculars. The three stars at the top areOrion’s belt, and the stuff near the lower left corner of the pictureis known as his sword — to the naked eye, it just looks like threemore stars that aren’t as bright as the stars in the belt. The middle“star” of the sword, however, isn’t a star at all. It’s a cloudof gas, known as the Orion Nebula, that’s in the process of collapsingdue to gravity. Like the pool skater on his way down, thegas is losing gravitational energy. The results are very different,however. The skateboard is designed to be a low-friction device,so nearly all of the lost gravitational energy is converted to kineticenergy, and very little to heat. The gases in the nebula flowand rub against each other, however, so most of the gravitationalenergy is converted to heat. This is the process by which starsare born: eventually the core of the gas cloud gets hot enough toignite nuclear reactions.Lifting a weight example 8⊲ At the gym, you lift a mass of 40 kg through a height of 0.5m. How much gravitational energy is required? Where does thisenergy come from?⊲ The strength of the gravitational field is 10 joules per kilogramper meter, so after you lift the weight, its gravitational energy willbe greater by 10 × 40 × 0.5 = 200 joules.Energy is conserved, so if the weight gains gravitational energy,something else somewhere in the universe must have lost some.The energy that was used up was the energy in your body, whichcame from the food you’d eaten. This is what we refer to as“burning calories,” since calories are the units normally used todescribe the energy in food, rather than metric units of joules.24 Chapter 1 Conservation of Mass and Energy